Bounding Free Energy Difference with Flow Matching

We introduce a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free energy estimation based on targeted free energy perturbation by performing calculations on samples from both ends of the mapping. We demonstrate applications of the present method by estimating the free energy of a classical Coulomb gas in a harmonic trap.